Dirac’s delta function

Definition

$\delta (x)=\{\begin{array}{ll}\infty & t=0\\ 0& t\ne 0\end{array}=\underset{k\to 0}{\lim }{f}_k(t)=\{\begin{array}{ll}\frac{1}{k}& 0\le t\le k\\ 0& \text{otherwise}\end{array}$ $\delta (t-a)=\{\begin{array}{ll}\infty & t=a\\ 0& t\ne a\end{array}=\underset{k\to 0}{\lim }{f}_k(t-a)$

Facts

${\int }_0^{\infty }\delta (t-a)g(t)dt=g(a)$